A Universally derided "primality test".

[RMLabrador]

I can explain why this test do not suffer for flaw of modulo computation.

[RMLabrador]

I can explain why this test do not suffer modulo flaw.

[paulunderwood]

Originally Posted by RMLabrador

Attachment 23318
I can explain why this test do not suffer for flaw of modulo computation.

{forstep(n=9,77,2,
if(!ispseudoprime(n),
for(u=round(log(n)^2),n,
A=Mod(Mod([1+i,1;1,u],n),i^2+1);
X=A^n;
R=lift(lift(trace(X*i)))%i;
if(R==1||R==n-1,
print([n,u,R])))))}
[25, 11, 24]
[25, 12, 24]
[25, 16, 24]
[25, 17, 24]
[25, 21, 24]
[25, 22, 24]
[49, 15, 48]
[49, 21, 48]
[49, 22, 48]
[49, 28, 48]
[49, 29, 48]
[49, 35, 48]
[49, 36, 48]
[49, 42, 48]
[49, 43, 48]
[49, 49, 48]
[65, 20, 64]
[65, 22, 1]
[65, 30, 64]
[65, 33, 64]
[65, 41, 1]
[65, 43, 64]
[65, 59, 64]
[65, 61, 1]
[77, 25, 76]
[77, 44, 76]
[77, 58, 76]

You test works for some composites too.

Besides it makes no sense to use an inequality symbol when working with modular arithmetic.

[RMLabrador]

ok. Key in the u value. Let them bigger! I'm put log^2 without deep thinking, there is some value, after all be ok.
Just let u=1000000 and see result
Believe me

P/S
Results are oscillating for the small u and for prime numbers go stable
after some u
For all other numbers for every u we got another result
so if You found "exception" just
test u+1

[paulunderwood]

That might take some time

However:

{forstep(n=1001*1001,100000000,2,
if(!ispseudoprime(n),
for(u=1000000,n,
A=Mod(Mod([1+i,1;1,u],n),i^2+1);
X=A^n;
R=lift(lift((trace(X*i))))%i;if(R==1||R==n-1,
print([n,u,R]);break(2)))))}
[1002001, 1000000, 1002000]

You can play with this code by installing pari-gp if you have linux or by getting Pari/GP for windows at this site.

[RMLabrador]

make test for u+1 for this case
Thank You for the link!

[RMLabrador]

At any rate, I am convinced that He [God] does not play dice./ Albert Einstein

As mentioned, God do not play dice. Its true, I am convinced that He play Cards instead. /Roman V. Makarchuk

Remember this.
If we want to build skyscraper (of math) taller, we need good basement, isn't?
Somebody know the rules of factors in numbers, their appearing, emerging, combination,
I mean the RULES? We play the game in the blind state)

For proof this simple test. we need to go deep below, to the kernel foundation, away of high grade construction, no matter how shiny wise or flying so mathematical high they are.

test in this form still have probability nature, for every non prime number for any u chance of false exception 2/n where n is testing number. For u, u+1 - 4/n^2 and so on, for big numbers this goes to zero very fast.
Repeated modulo operation erase the (easy) way to make the test deterministic,
once again that arise form modulo computation. Just see the oscillation of result with only one modulo operation in the last step, you can do this for the small n~0-10000
P/S
You may ask me about the proof.

[paulunderwood]

Originally Posted by RMLabrador

At any rate, I am convinced that He [God] does not play dice./ Albert Einstein

As mentioned, God do not play dice. Its true, I am convinced that He play Cards instead. /Roman V. Makarchuk

God may not play dice with the universe, but something strange is going on with the prime numbers -- Paul Erdos

[RMLabrador]

I'm one, who know.
I'm reveal the part (of rules) and they resembling the card game)
I can proof of this my claim for now, but just like recurrent sequence represent deferential equation, mention above will be represent of equation (of quantum mechanic) and above.
So. if somebody wold like became the part of the history and have a some math level -
you ale welcome.
I have an unlimited amount of ideas, and, I suspect, no time.
So, check this test first.
or message me, and we discuss the proof of Riemann hypothesis - my ideas, your write in good English.

[LaurV]

The fact that god plays dice or not or she is scratching her ass (i mean donkey) is non sequitur. The test is just PRP in disguise.

[RMLabrador]

Well, I'm explain why, not my fault if someone do not understand or do not at least check this out. This is my poor English. For the small u values, if we rise matrix to power without of modulo on the every step, and do it only one time, in the end, the result for prime and not prime numbers ARE deterministic, and, in general, is result of computing limitation or more precise, on the difference between analytical and numerical computation.
if You look why this test work, you understand my point.